All I Ever Wanted to Know About Circles

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1 Parts of the Circle: All I Ever Wanted to Know About Circles Important Circle Vocabulary: CIRCLE- the set off all points that are the distance from a given point called the CENTER- the given from which all points on a are the same RADIUS- the distance from the of a circle to any point on the circle DIAMETER- the across a circle through its CIRCUMFERENCE- the around a AREA- the amount of space contained of the circle

2 Calculating Circumference: c = 2 r Example 1: Pi Calculate the circumference of the given circle. 7.2 cm Circumference of a circle: c = 2 r Q: What is Pi? A: Pi is a symbol representing a number that has been calculated out to over 1 million decimal places without stopping or repeating ( )!! To save space, we just use the Greek symbol (sounds like pie spelled like pi). Replace r with 7.2: Use a calculator: Example 2: Calculate the circumference of the given circle. 9 cm If d = 9, r must equal? Circumference of a circle: c = 2 r Replace r with 4.5: Use a calculator:

3 Practice Problems (circumference): Find the circumference of each circle. Round your answer to the nearest tenth and include units in 24 mm 38 mi km 19.4 m 7.25 ft Solve (include units). If needed, round to the nearest hundredth. 7. If the tire on a car has a diameter of 25 inches, how far will the car travel each time the tire completes one rotation? 8. A hiker wants to walk around a circular lake. If the distance from one side to the other is 200 yards, how long will the hike be? 9. A tree has a diameter of 3 feet. How big around is the tree? 10.A tetherball is tied to a pole with a 1.5 meter rope. How far will the ball travel if it swings completely around the pole?

4 Calculating Area of a Circle: A = r 2 Example 1: Calculate the area of the given circle. 2.7 cm Area of a circle: A = r 2 Replace r with 2.7: Solve: Approximate with a calculator: Example 2: Calculate the area of the given circle. 5 in If d = 5, r must equal? Area of a circle: A = r 2 Replace r with 2.5: Solve: Approximate with a calculator:

5 Practice Problems (area): Find the area of each circle. Round your answer to the nearest tenth and include units in 24 mm 38 mi km 19.4 m 7.25 ft Solve (include units). If needed, round your answer to the nearest hundredth. 9. What is the area, in square inches, of a medium 14 inch pizza from the Green Hills deli? 10.Two friends want to fish a circular lake. If the distance from the center of the lake to shore is 300 yards, how large is the lake? 9. A worker needs to carpet a circular room. If the distance across the room is 15 feet, how much carpet will be needed? 10.A California ground squirrel usually stays within 150 yards of its burrow. Find the area of the ground squirrel's world.

6 What if I Already Know the AREA or CIRCUMFERENCE??? STEP 1: decide whether you need the area or circumference formula and write it down STEP 2: substitute the known values from the problem into the formula STEP 3: solve (hint... just like one & two step equations!!) Example 1: Find the radius of the given circle. A = 16 Area of a circle: A = r 2 Replace A with 16 : Solve: Example 2: Calculate the diameter of the given circle. c = 44 ft Circumference of a circle: c = 2 r Replace c with 44: Solve:

7 Practice Problems (known circumference or area): 1. Find the radius of a circle whose area is Find the diameter of a circle whose circumference is 40 feet. Round your answer to the nearest hundredth. 3. Find the radius of a circle whose circumference is 68 inches. Round your answer to the nearest tenth. 4. Find the radius of a circle whose area is If the circumference of a circle is 628 cm, what is the diameter of that circle?

8 6. If the circumference of a circle is 400 cm, what is the radius of that circle? 7. The circumference of the circle below is centimeters, what is the best estimate for the length of the radius? 8. A circle has a circumference that measures 18 inches. What is the radius, in inches of the circle? 9. Find the length of the radius of each circle given the following areas. a. 400 b. 625 c. 16

9 Who Discovered, anyway?... Group Members Directions: You will need one ruler, one piece of string, and the circular objects, which I will be giving you. First: Record which item you are using Second: Wrap the string around the outside of the object and hold the string up to the ruler to measure the circumference. Record the circumference in the table. Third: Stretch the string from one side of the object to the other to measure its diameter. Hold the string up to the ruler, and record the diameter in the table. Fourth: Move on to your next object! Data Collection Item Measured Circumference Diameter C d The more accurate you measure your circumference and diameter, the closer c d will resemble, the number we call!!!

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